Updated Tuesday at 6:29 p.m. to include new comments from board Chairwoman Patricia Devine and Mayor Alex Morse, comments from board member James Brunault and City Councilor Todd McGee and background information.

A dispute also exists about the size of the debt, with some officials saying it is $2.2 million and others contesting parts of that total.

The payment plan the authority board approved is only for $465,000 in employee-retirement costs, board member James Brunault said Tuesday. The city in December paid those costs, which had gone unpaid since 2008.

The authority is current on pension payments made from employee payroll deductions, but has struggled with its own pension contributions.

The authority would pay the city $500 a month for six months and $750 a month beginning in January. A review in July 2013 would determine the next increase, board Chairwoman Patricia C. Devine wrote in an email.

“Although it is not a huge amount, it was done in good faith, as promised, and hopefully increases will keep occurring,” Devine wrote.

“I believe this is the first time that any board has made the strides in repayment as we have done,” she wrote.

As of Monday, the authority’s debt is $2,224,959 to the Retirement Board and Holyoke Gas and Electric Department, as well as for health and life insurance and for payments to the city in lieu of taxes, City Treasurer Jon D. Lumbra said.

Brunault said the authority has a separate payment plan with the Gas and Electric Department on which $25,000 has been paid. Lumbra said the authority owes the utility nearly $428,000.

Authority officials, including board member Joseph T. O’Neill, when he was chairman last year, have disputed whether the authority owes the city for health and life insurance payments for retired authority employees. According to Lumbra, the authority owes the city $988,448 for that dating back to 2007.

Regarding another $120,000 that Lumbra said the authority owes the city for payments in lieu of taxes, dating back to 2009, Brunault said his understanding was officials are trying to work out that issue.

The authority is a nursing home that has 80 beds and 80 other slots for the daycare of senior citizens at 45 Lower Westfield Road.

It is overseen by a board consisting of three appointed by the City Council and three appointed by the mayor, with those six choosing a seventh.

The authority has struggled with thinning revenues as federal reimbursements for the care it provides its residents has covered only 75 percent of costs.

Todd A. McGee, council Finance Committee chairman, said councilors will keep monitoring the authority. The current board deserves credit for paying current bills, cutting costs and providing a payment plan, whatever its size, he said.

“Is is the best step? No, but it’s a start,” McGee said.

Devine, a former councilor, joined the board and was voted chairwoman April 25. She was one of three new members.

But Morse said a difficult discussion about the authority’s future is necessary because he’s not convinced a municipality should be running a nursing home.

Repaying taxpayers should be the authority’s priority, he said, but the board’s payment plan was done without negotiations with the city.

“The proposal presented to me by Ms. Devine is unsatisfactory....Their proposal won’t come close to putting a dent in the $2.2 million dollars that the (authority) owes the city,” Morse said.

“If the (authority) doesn’t demonstrate financial solvency in the near future, action must be taken,” he said, adding later, “It’s nobody’s fault, it’s the system.”

With strong talk from the mayor about the authority’s future, Devine was asked for reaction to that and wrote in an email, “We continue to find ways to cut costs without putting the residents in fear of closing, or the dedicated staff in fear of losing their jobs as the mayor has just done with his comments.”